The anomalous Hall effect in ferromagnetic conductor is considered to come from three different contributions, and the AHC can be expressed as \(\sigma _{H}^A = \sigma _{int} + \sigma _{sk} + \sigma _{sj}\) , where \(\sigma _{int}\)  is the intrinsic contribution, and \(\sigma _{sk}\)  and \(\sigma _{sj}\)  are the parts come from screw scattering and side jump mechanisms, respectively [1]}. Both of the \(\sigma _{sk}\)  and \(\sigma _{sj}\)  terms are the consequences of extrinsic scattering from disorder or impurities, while the \(\sigma _{int}\)  term depends only on the band structure. Figures REF (a) and (b) show the anomalous parts of the Hall conductivity \(\sigma _{zx}\)  and \(\sigma _{xy}\) , respectively, which are obtained by \(\sigma _{ij} = \rho _{ji}/(\rho _{ji}^2+\rho _{ii}^2)\) . To extract the intrinsic contribution of the AHC, we employ the so-called Tian-Ye-Jin (TYJ) scaling [2]}, [3]}: \(\sigma _{xy}^A = a\sigma _{xx}^2+\sigma _{xy}^{int}\) , where \(a\)  is a system relevant constant, and \(\sigma _{xy}^{int}\)  is the intrinsic AHC contribution. Figures REF (c) and (d) show the AHC as the function of \(\sigma _{xx}^2\)  for the two directions. The intrinsic contribution of AHC can be obtained from the intercept of the fitting line, which is 170 \(\Omega ^{-1}\)  cm\(^{-1}\)  and 380 \(\Omega ^{-1}\)  cm\(^{-1}\)  for \(\sigma _{zx}^{int}\)  and \(\sigma _{xy}^{int}\) , respectively. This anisotropic intrinsic AHC suggests the influence of magnetic field direction on the electronic structure of LiMn\(_6\) Sn\(_6\)  again. The value of \(\sigma _{xy}^{int}\)  can be converted into 0.88 \(e^2/hc\) , where \(c\)  is the cross-plane lattice constant. Considering there are two kagome Mn layers in a unit cell, it gives 0.44 \(e^2/h\)  per Mn layer. This intrinsic Hall conductivity component in LiMn\(_6\) Sn\(_6\)  is much larger than those that have been found in the \(R\) Mn\(_6\) Sn\(_6\)  compounds with ferrimagnetic order, such as 0.27 \(e^2/h\)  per Mn layer for GdMn\(_6\) Sn\(_6\) , and 0.14 \(e^2/h\)  per Mn layer for TbMn\(_6\) Sn\(_6\) , as listed in Table REF .
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